Question

y+1/y=12then y3+1/y3=

Answer 1

Given y + 1/y = 12.   ------ (1)

On Squaring both sides, we get

We know that (a + b)^2 = a^2 + b^2 + 2ab.

Then (y + 1/y)^2 = (12)^2

         y^2 + 1/y^2 + 2 * 1/y = 144

         y^2 + 1/y^2 + 2 = 144

         y^2 + 1/y^2 = 144 - 2

        y^2 + 1/y^2 = 142.   ----------- (1)




Given y^3 + 1/y^3.

We know that a^3 + b^3 = (a+b)(a^2 +b^2 - ab)

Here a = y^3, b= 1/y.

y^3 + 1/y^3 = (y+1/y)(y^2 + 1/y^2 - y * 1/y)

                   = (y + 1/y)(y^2 + 1/y^2 - 1) 

                   = (12)(142 - 1) (From (1) and (2))

                   = 12 * 141

                  = 1692.


Therefore y^3 + 1/y^3 = 1692.


Hope this helps!